write the equation of a line that is perpendicular to y=3x-2 that passes trough the point (-9,5)
Answers
Important takeaway is that the slopes of two perpendicular lines are always negative reciprocals.
[tex]\huge\boxed{y-5&=-\frac{1}{3}(x+9)}[/tex]
First, we'll find the slope of the new line. The first line has a slope of [tex]3[/tex]. Take the negative reciprocal of this (Flip the numerator and denominator, then multiply by [tex]-1[/tex]) to get [tex]-\frac{1}{3}[/tex] for the new slope.
Then, we'll use the point-slope form to make the new equation, where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] is a point on the line:
[tex]\begin{aligned}y-y_1&=m(x-x_1)\\y-5&=-\frac{1}{3}(x-(-9))\\y-5&=-\frac{1}{3}(x+9)\end{aligned}[/tex]
Related Questions
60. Cities A and B are on the same east-west line.
Assume that city A is located at the origin. If the
distance from city A to city B is at least 100 miles
and x represents the distance from city B to city A,
express this using absolute value notation.
Answers
Answer:
The expression for the statement using absolute value notation is [tex]|x|\geq 100[/tex]
Step-by-step explanation:
It is given in the question that the distance from city A to city B is at least 100 miles.
It is required to express the statement using absolute value notation.
To express the statement using absolute value notation, deduce the statement in the form of an equation.
x represents the distance from city B to A city .
Deduce the statement in the form of an equation
[tex]|x|\geq 100[/tex]
Please help with a rational functions equation question.
Answers
If a store sold 25 pairs of socks, making a 25% profit (i.e., percent of sales) of $150, how much did they charge for each pair
Answers
The store charged $24 for each pair of socks as the selling price.
What is Profit?Profit is the financial gain that is earned by a business or an individual after deducting all expenses from revenue. In other words, it is the amount of money that remains after all costs of producing and selling a product or service have been subtracted from the total revenue earned.
What is Revenue?Revenue refers to the total amount of income earned by a business or an individual from the sale of goods or services during a specific period of time. It is the total amount of money that a business receives from its customers in exchange for its products or services.
In the given question,
Let's start by calculating the total revenue from the sale of 25 pairs of socks
Since the profit is 25% of the revenue, we can set up the equation:
Profit = 0.25 * Revenue
$150 = 0.25 * Revenue
Revenue = $150 / 0.25
Revenue = $600
The total revenue from selling 25 pairs of socks is $600.
To find the price per pair of socks, we can divide the revenue by the number of pairs:
Price per pair = Revenue / Number of pairs
Price per pair = $600 / 25
Price per pair = $24
Therefore, the store charged $24 for each pair of socks.
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A translation is shown on the grid below. On a coordinate plane, triangle A B C has points (negative 4, 2), (negative 4, negative 2), (negative 1, negative 2). Triangle A prime B prime C prime has points (1, 5), (1, 1), (4, 1). Which are true statements about the translation? Select 3 options. The sides of the image and pre-image are congruent. The image is turned 90°. The angles in the image are different from the angles in the pre-image. The image is a slide of the pre-image. The image has a different shape than the pre-image. Each point has moved in a different direction. Each point has moved the same number of units.
Answers
Based on the translated image and the original triangle ABC, the true statements are:
The sides of the image and pre-image are congruent.The image is a slide of the pre-image.Each point has moved the same number of units.What can be said of the translation?The pre-image of triangle ABC and the image are shown to have sides that are congruent because they are exactly the same. This is why triangle A¹B¹C¹ is a slide of triangle ABC.
In order to form the image, the translation must have been such that each point of the preimage moved the same number of units.
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Answer:
a, d, g
Step-by-step explanation:
i took da test
A measure of the strength of the relationship between two variables is referred to as the.
Answers
A measure of the strength of the relationship between two variables is referred to as the correlation coefficient.
What is the correlation coefficient?To gauge the strength of the linear link between two variables, correlation coefficients are used.
A value of correlation coefficient less than zero denotes a negative association, while a value greater than zero denotes a positive relationship.
A zero correlation coefficient means there is no correlation between the two variables under comparison.
A crucial idea in building diversified portfolios that may better resist portfolio volatility is the concept of a negative correlation, often known as an inverse correlation.
Since calculating the correlation coefficient takes time, it is frequently done by entering data into a calculator, computer, or statistics application.
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The midpoint of AB is M (5, 6). If the coordinates of A are (3, 8), what are the
coordinates of B?
Answers
Answer:
(7, 4)
Step-by-step explanation:
[tex]\text{Let the coordinates of B } = x_{B} , y_{B} \\\text{Let the coordinates of A} = x_{A} , y_{A} \\\text{Let the coordinates of midpoint M} = x_{M} , y_{M}[/tex]
By the midpoint formula,
[tex](x_{M},y_{M}) = (\frac{x_{A} + x_{B}}{2} , \frac{y_{A} + y_{B}}{2} )[/tex]
[tex]x_{M} = \frac{x_{A} + x_{B}}{2} \\y_{M} = \frac{y_{A} + y_{B}}{2} \\[/tex]
We have coordinates of midpoint as (5, 6) and coordinates of A as (3,8)
So
[tex]5 = \frac{3 + x_{B}}{2} \\\\\\textrm{Cross-multiplying } 10 = 3 + x_{B}} \textrm{ or } x_{B} = 10-3 = 7\\[/tex]
[tex]6 = \frac{8 + y_{B}}{2} \\\\\\\\textrm{Cross-multiplying } 12 = 8 + y_{B}} \textrm{ or } y_{B} = 12-8 = 4\\[/tex]
So coordinates of B are (7,4)
what’s the slope of a line using (-5, -4) and (-7, -6)
Answers
Answer: 1
Step-by-step explanation:
To find slope: (y1-y2)/(x1-x2)
y1 = -4
y2=-6
x1 = -5
x2 = -7
-4 --6 = -4 + 6 = 2
-5--7 = -5+7 = 2
2/2 = 1
so, the slope is 1
any sample proportion that is more than 1.96 standard errors from the popullation proportion will result in an
Answers
Any sample proportion that is more than 1.96 standard errors from the population proportion will result in a confidence interval that includes p.
In frequentist records, a confidence interval is more than a few estimates for an unknown parameter. A self-belief interval is computed at a chosen self-belief stage; the ninety-five% self-assurance stage is maximum commonplace, however other tiers, which include ninety% or ninety-nine%, are now and again used.
The confidence stage is the share of instances you expect to get near the identical estimate if you run your test again or resample the populace in an identical manner.
The confidence c programming language includes the higher and lower bounds of the estimate you anticipate locating at a given stage of confidence.
As an instance, in case you are estimating a 95% self-belief c language around the mean share of lady toddlers born every 12 months primarily based on a random sample of babies, you may find a top certain of zero.56 and a decrease certain of zero.48. those are the top and decrease bounds of the self-belief c programming language. The self-assurance level is 95%.
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Mrs. Hamilton shows her students this graph and asks them to determine how figure A was transformed to figure B.
On a coordinate plane, triangle A has points (negative 1, 0), (negative 2, 4), (negative 1, 4). Triangle B has points (3, 1), (3, 5), (4, 5)..
Marcus suggests that figure A was reflected over the y-axis and then translated 2 to the right and 1 up. Julianne agrees, and states that the transformations could happen in any order. Which best describes the accuracy of Julianne’s statement?
Accurate. A translation of figure A of 2 to the right and 1 up and then a reflection over the y-axis produces the image, figure B.
Accurate. A reflection over the y-axis and then a translation of 1 up and 2 to the right produces the image, figure B.
Inaccurate. A translation of 2 to the right and 1 up and then a reflection over the y-axis results in a figure that is located in the second quadrant.
Inaccurate. A reflection over the y-axis and then a translation of 1 up and 2 to the right results in a figure that is located in the second quadrant.
On a coordinate plane, triangle A has points (negative 1, 0), (negative 2, 4), (negative 1, 4). Triangle B has points (3, 1), (3, 5), (4, 5)
Answers
The best accuracy for the transformation is; Accurate. A reflection over the y-axis and then a translation of 1 up and 2 to the right produces the image, figure B.
What transformation was used on the figure?
In a translation transformation, all the points in the object are moved in a straight line in the same direction. The size, the shape and the orientation of the object remain the same.
In this question, the points on triangle A are: (-1, 0), (-2, 4) and (-1, 4).
Marcus' translation is as follows:
Reflection over the y-axis which is x → -x and the points are: (1,0), (2,4) and (1,4).2 units to the right which is x → x + 2 and as such the points are: (3, 0), (4,4) and (3,4).1 unit up which is y → y + 1 and as such, the points are (3,1), (4,5) and (3,5).The points are the same of triangle B, hence the statement is accurate. According to the order of the translations, the second statement is correct.
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If x+y=6,y+z=7, z+x=9 what is the average or x, y and z
Answers
Step-by-step explanation:
so in this case
x-4
y-2
z-5
average=x+y+z/no of values
= 4+5+2/3
=11/3
=3.6
The function below models the correlation
between the number of hours a plant is kept in
sunlight (x) and the height (y), in mm, to which it
grows:
y = 2 + 4x
What does the y-intercept of this function
represent?
The original height of the plant was 4 mm.
The original height of the plant was 2 mm.
The height of the plant increases by 2 mm for
every hour of sunlight it receives.
The height of the plant increases by 4 mm for
every hour of sunlight it receives.
Answers
The graph of f(x) =[tex]2^{x+3}[/tex] shifts 10 units to the right when it is replaced with the graph of f(x) = [tex]2^{x-k}[/tex]. What is the value of k? 3 7 10 13
Answers
Answer:
7
Step-by-step explanation:
Whenever you shifting an exponential function to the left/right, you're going to generally have the equation: [tex]y=2^{x-k}[/tex] where k is the shift. So in this case we can think of x+3 as x and k as 10, since the shift is 10. This gives you the equation: (x+3) - 10, which simplifies to x-7, meaning the k value in this case is going go be 7. You can also think of it as already being shifted 3 units to the left, and you shift it 10 units to the right, that means this new function will be shifted 7 units to the right relative to the origin. This means the k=7.
The plane flew over a beacon which is 280 miles from bristol. write down the gmt times when the plane flew over the beacon.
Answers
According to graph, GMT time when the plane flew over the beacon was 9:24.
While looking closely at the graph on x axis , one will notice that each hour is divided into 5 parts and hence each part has 12 minutes. looking at y axis, one may find that each part on y axis resembles 20miles. Hence at 280 miles away from Bristol, The GMT time is 9:24.
What is a graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.The relationships between two or more items are frequently represented by the points on a graph.The study of graphs, which are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. Vertices (also known as nodes or points) make up a graph in this sense, which are connected by edges (also called links or lines).Undirected graphs, in which edges connect two vertices symmetrically, are distinguished from directed graphs, in which edges connect two vertices asymmetrically. One of the main topics of study in discrete mathematics is graphs.Know more about graph numerical
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hallar el valor de ab datos: bc= 4,5 cm de= 2cm ef= 3 cm
Answers
The measure of ab and df are 3cm and 7.5cm respectively
Similarity theorem of shapesIn order to determine the missing sides, we need to take the ratio of the similar sides as shown:
1) ab/de = ac/df
ab/de = ab+bc/df
Substitute the given values
ab/2 = ab+4.5/2+3
ab/2 = ab+4.5/5
2(ab+4.5) = 5ab
2ab+9=5ab
3ab = 9
ab = 3cm
Hence the measure of ab is 3cm
2) ae/ce = bf/df
24/9 = 20/df
24df =. 9(20)
24df = 180
df = 7.5cm
Hence the measure of ab and df are 3cm and 7.5cm respectively
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There are between 90 and 115 cars in a parking lot. Exactly one-fourth of them are green. Exactly one-eighth of them have a sticker on the back that says, Mr. Donovan is the best teacher ever. How many cars MIGHT be in the parking lot
Answers
There are 104 cars in the parking lot.
According to statement there are between 90 and 115 cars on the lot.
So, {X| 90 < x < 115} (This renders an infinite solution set finite)
AND exactly one eight of them have a sticker on the back, so the total number of cars must be evenly divisible by eight.
X ∈ {96, 104, 112,}
AND exactly one fourth of the cars are green, so the number of cars must be evenly divisible by 4. Here all above written numbers are divisible by 4. So, find the mean to calculate the number of cars in the parking lot.
x = (96+104+112)/3
x = 104
There are 104 cars in the parking lot.
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The Westminster Widget Company has an old machine that can produce 50 widgets in five hours. Now they have purchased a
new machine that can produce 30 widgets in two hours. Working together, how long will it take the two machines to produce
100 widgets?
4 hours
16 hours
hour
8 hours
Answers
Answer:
If they worked together it would take 4 hours for the machines to produce 100 widgets
Step-by-step explanation:
w = widgets hr = hour ph = per hour
Old machine - 50w = 5hr = 10ph
New machine - 30w = 2hr = 15ph
Old machine - 20w = 2hr
New machine - 30w = 2hr
Together - 50w = 2hr x 2 Final: 100w = 4hrI hope this helped!
What is the 6th term of the geometric sequence where a1 = −4,096 and a4 = 64
Answers
The 6th term of the sequence is 4
How to determine the 6th term?The given parameters are:
a1 = -4096
a4 = 64
The nth term of the sequence is:
a(n) = a1 * r^(n-1)
So, we have:
a4 = a1 * r^3
This gives
r^3 = a4/a1
Substitute the known values
r^3 = 64/-4096
Evaluate
r^3 = -1/64
Take the cube roots
r = -1/4
The 6th term is
a(6) =a1 * r^5
This gives
a(6) = -4096 * (-1/4)^5
Evaluate
a(6) = 4
Hence, the 6th term of the sequence is 4
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Solve for y 3x+3-x+ (-7) > 6 o a. x > (-5) b. x<5 ) cy>5 ) d. x > 2.5
Answers
The value of x for the inequality 3x+3-x+ (-7) > 6 is x > 5. This a can be obtained by solving the linear inequality by taking terms with x to one side of the inequality similar to solving of linear equation.
What is the value of x?Given that
3x + 3 - x + (-7) > 6
3x - x > 6 + 7 - 3
2x > 10
x > 5
Hence the value of x for the inequality 3x+3-x+ (-7) > 6 is x > 5. The correct option is c.
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i need help on this question for algebra
Answers
Answer:
36 miles and 10 miles
Step-by-step explanation:
area = length × width
A = LW
W = unknown = x
L = 26 ft more than width = x + 26
A = LW
360 = (x + 26)x
360 = x² + 26x
x² + 26x - 360 = 0
(x + 36)(x - 10) = 0
x + 36 = 0 or x - 10 = 0
x = -36 or x = 10
We discard the solution x = -36 since the width of a rectangle cannot be a negative number.
W = x = 10
L = x + 26 = 10 + 26 = 36
Answer: 36 miles and 10 miles
What is the slope in the equation y = 2x + 3
Answers
un bibliotecario de la biblioteca "Amauta" coloca libros de aritmética y álgebra en un estante, notando que la relación de libros de aritmética y el total de libros es de4 a 9. respectivamente Si sabe que coloca 10 libros de álgebra en el estante
¿Cuántos libros de aritmética coloca la bibliotecaria?
Answers
Concluimos que hay 8 libros de aritmética.
¿Cuántos libros de aritmética coloca la bibliotecaria?
Sabemos que la relacion entre el número de libros de aritmetica y el total de libros es de 4 a 9.
Es decir, sí el número total de libros es N, entonces (4/9)*N de esos libros son de aritmética.
Sea X el número de libros de aritmética. Sabemos que hay 10 libros de algebra, entonces el número total N es:
N = 10 + X
Y usando la relación de arriba, podemos escribir:
X = (4/9)*N = (4/9)*(10 + X)
Ahora podemos resolver esto para X.
X*(9/4) = 10 + X
X*(9/4) - X = 10
X*(5/4) = 10
X = (4/5)*10 = 8
Concluimos que hay 8 libros de aritmética.
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the graph of f(x)=3x what is the value of x when f(x)=9
Answers
Answer:
[tex]\{3\}[/tex]
Step-by-step explanation:
Strictly speaking, we need to know the point of [tex]f(x) = 3x[/tex] intersecting [tex]f(x) = 9[/tex]. In other words, we need to solve the equality:
[tex]3x = 9; \\ x = \frac{9}{3}; \\ x = 3[/tex]
Here it is.
Given ƒ(x) = x + 10, find ƒ(x + 1).
Answers
Work Shown:
f(x) = x + 10
f(x+1) = x+1 + 10 .... replace every x with x+1
f(x+1) = x + 11
A machine can pump 15 litres of water in one minute.
How long does it take to pump 900 litres of water
Answers
Answer:
900 liters of water is pumped in 1 hour
Step-by-step explanation:
Time taken to pump 15 liters of water = 1 minute.
Time taken to pump 1 liters of water = 1/15 minute
[tex]\sf \text{Time taken to pump 900 liters of water=$\dfrac{1}{15}*900$}[/tex]
= 60 minutes
= 1 hour
How many different ways
can you arrange the letters
in the word SMILE?
PLSSS HELP
Answers
Answer:
120 different ways
Step-by-step explanation:
The formula to count the permutation since the order the matters: nPr = n! / (n - r)!, where n is the total number and r is the total number of chosen.
1) Substitute values into the formula. SMILE has 5 letters, and we choose 5.
5P5 = 5! / (5 - 5)!
5P5 = 5! / 0!
Zero factorial (0!) is always 1.
So, 5P5 = 5! / 1
5! = 5 × 4 × 3 × 2 × 1
5! = 120
Therefore, 5P5 = 120 / 1, which is 120. We can arrange the word SMILE in 120 different ways.
18. For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line
2. Is each pair of lines parallel, perpendicular, or neither?
18. Line 1: Passes through (0, 6) and (3, -24 Line 2: Passes through (-1, 19) and (8, -71)
Answers
Answer:
The given lines are parallel.
Step-by-step explanation:
In the question, two lines are given as line 1 passes through (0,6) and (3,-24). Whereas, line 2 passes through (-1,19) and (8,-71).
It is required to find the slope of given lines and figure out whether they are perpendicular, parallel or neither.
To solve this question, first find the slope of both lines. Check if their product is equal to -1, then they are perpendicular. If the slopes are equal the lines are parallel
Step 1 of 2
Find the slope of first line.
[tex]$$\begin{aligned}&m_{1}=\frac{-24-6}{3-0} \\&m_{1}=\frac{-30}{3} \\&m_{1}=-10\end{aligned}$$[/tex]
Step 2 of 2
Find the slope of first line.
[tex]$$\begin{aligned}&m_{2}=\frac{-71-19}{8-(-1)} \\&m_{2}=\frac{-90}{9} \\&m_{2}=-10\end{aligned}$$[/tex]
Since, both slopes are equal.
Therefore, the lines are parallel.
Writing Exercises
353. Why does (a + b)² result in a trinomial, but (a − b)(a + b) result in a binomial?
Answers
Answer:
In [tex]$(a+b)^{2}$[/tex] is obtained by addition therefore result is trinomial while in (a-b)(a + b) the middle terms are canceled out of each other therefore result is binomial.
Step-by-step explanation:
Explanation
Given that [tex](a+ b)^{2}$[/tex] results in a trinomial, but (a-b)(a-b) results in a binomial.An expression [tex]$(a+b)^{2}$[/tex] when multiply and simplify it is equal [tex]a^{2}+a b+a b+b^{2}=a^{2}+2 a b+b^{2}$[/tex] therefore it is trinomial. Here middle term is obtained by addition. While an expression (a + b) (a-b) when multiply and simplify it is equal to [tex]$a^{2}-a b+a b+b^{2}=a^{2}+b^{2}$[/tex]therefore it is binomial because the middle that is positive ab is canceled by negative ab.Find the two straight lines represented by x² + 5xy - 6y² = 0
Answers
By factorizing, we have
[tex]x^2 + 5xy - 6y^2 = (x - y) (x + 6y) = 0[/tex]
so that
[tex]x - y = 0 \implies \boxed{y = x}[/tex]
or
[tex]x + 6y = 0 \implies \boxed{y = -\dfrac x6}[/tex]
Suppose that 43% of the people who inquire about investments at a certain brokerage firm end up investing in stocks, 38% end up investing in bonds, and 51% end up investing in stocks or bonds (or both). What is the probability that a person who inquires about investments at this firm will invest in both stocks and bonds?
Answers
What is the length of the side opposite the 45° angle?
Answers
Answer:
Step-by-step explanation:
c = b·sin(C)
c= 10Sin(45
c=7.071
So the side length opposite to the 45 degree angle is 7.071 :)
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